• Structural Engineering and Mechanics
• /
• v.64 no.6
• /
• pp.695-701
• /
• 2017

This paper investigates some general properties in the degenerate scale problem of antiplane elasticity or Laplace equation. For a given configuration, the degenerate scale problem is solved by using conformal mapping technique, or by using the null field BIE (boundary integral equation) numerically. After solving the problem, we can define and evaluate the degenerate area which is defined by the area enclosed by the contour in the degenerate configuration. It is found that the degenerate area is an important parameter in the problem. After using the conformal mapping, the degenerate area can be easily evaluated. The degenerate area for many configurations, from triangle, quadrilles and N-gon configuration are evaluated numerically. Most properties studied can only be found by numerical computation. The investigated properties provide a deeper understanding for the degenerate scale problem.

• Journal of applied mathematics & informatics
• /
• v.37 no.3_4
• /
• pp.259-270
• /
• 2019

In this paper we define the degenerate Carlitz-type q-Euler polynomials by generalizing the degenerate Euler numbers and polynomials, degenerate Carlitz-type Euler numbers and polynomials. We also give some interesting properties, explicit formulas, a connection with degenerate Carlitz-type q-Euler numbers and polynomials.

• Communications of the Korean Mathematical Society
• /
• v.36 no.1
• /
• pp.19-26
• /
• 2021

Degenerate versions of the special polynomials and numbers since they have many applications in analytic number theory, combinatorial analysis and p-adic analysis. In this paper, we define the degenerate poly-Euler numbers and polynomials arising from the modified polyexponential functions. We derive explicit relations for these numbers and polynomials. Also, we obtain some identities involving these polynomials and some other special numbers and polynomials.

• Journal of applied mathematics & informatics
• /
• v.39 no.1_2
• /
• pp.1-11
• /
• 2021

In this paper, we define degenerate Carlitz-type twisted q-Euler numbers and polynomials by generalizing the degenerate Euler numbers and polynomials, Carlitz's type degenerate q-Euler numbers and polynomials. We also give some interesting properties, explicit formulas, symmetric properties, a connection with degenerate Carlitz-type twisted q-Euler numbers and polynomials.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.2
• /
• pp.569-579
• /
• 2016

L. Carlitz introduced higher order degenerate Euler polynomials in [4, 5] and studied a degenerate Staudt-Clausen theorem in [4]. D. S. Kim and T. Kim gave some formulas and identities of degenerate Euler polynomials which are derived from the fermionic p-adic integrals on ${\mathbb{Z}}_p$ (see [9]). In this paper, we introduce higher order degenerate Genocchi polynomials. And we give some formulas and identities of degenerate Genocchi polynomials which are derived from the fermionic p-adic integrals on ${\mathbb{Z}}_p$.

• Journal of applied mathematics & informatics
• /
• v.41 no.2
• /
• pp.331-343
• /
• 2023

In this paper, we give explicit identities for the degenerate q-poly-tangent numbers and polynomials. Finally, we obtain the relation of degenerate q-poly-tangent polynomials and Stirling numbers of the first kind and Stirling numbers of the second kind.

• Journal of applied mathematics & informatics
• /
• v.38 no.5_6
• /
• pp.427-438
• /
• 2020

In this paper we define a new degenerate Bell-Carlitz polynomials. It also derives the differential equations that occur in the generating function of the degenerate Bell-Carlitz polynomials. We establish some new identities for the degenerate Bell-Carlitz polynomials. Finally, we perform a survey of the distribution of zeros of the degenerate Bell-Carlitz polynomials.

• Journal of the military operations research society of Korea
• /
• v.27 no.1
• /
• pp.28-38
• /
• 2001

A transportation problem amy have multiple optimal solutions, if an optimal solution to the problem is degenerate. This study derives a condition, under which multiple degenerate optimal solutions exist, fro ma current degenerate optimal transportation tableau by utilizing the homogeneous equation obtained from the closed loops connecting degenerate basic variable and non-basic variables, and discusses a method of generating alternative degenerate optimal solutions and their associated transportation tableaus. Each degenerate optimal solution may not have the same range of feasibility in sensitivity analysis on supply and demand quantity due to different set of shadow prices which multiple degenerate solution have.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.5
• /
• pp.1427-1437
• /
• 2016

Cauchy polynomials are also called Bernoulli polynomials of the second kind and these polynomials are very important to study mathematical physics. D. S. Kim et al. have studied some properties of Bernoulli polynomials of the second kind associated with special polynomials arising from umbral calculus. T. Kim introduced the degenerate Cauchy numbers and polynomials which are derived from the degenerate function $e^t$. Recently J. Jeong, S. H. Rim and B. M. Kim studied on finite times degenerate Cauchy numbers and polynomials. In this paper we consider finite times degenerate higher-order Cauchy numbers and polynomials, and give some identities and properties of these polynomials.

• Communications of the Korean Mathematical Society
• /
• v.33 no.2
• /
• pp.651-669
• /
• 2018

The article is themed to classify new (fully) degenerate Hermite-Bernoulli polynomials with formulation in terms of p-adic fermionic integrals on $\mathbb{Z}_p$. The entire paper is designed to illustrate new properties in association with Daehee polynomials in a consolidated and generalized form.